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L ight A mplification by S timulated E mission of R adiation. Spontaneous emission. Stimulated emission. Lecture VIII. LASER. Energy level diagram. The possible energies which electrons in the atom can have is depicted in an energy level diagram. . T he operation of the Laser.

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Presentation Transcript
slide1

Light Amplification by Stimulated Emission of Radiation

Spontaneous emission

Stimulated emission

energy level diagram
Energy level diagram
  • The possible energies which electrons in the atom can have is depicted in an energy level diagram.
t he operation of the laser
The operation of the Laser
  • In 1958, Charles Townes and Arthur Schawlow theorized about a visible laser, an invention that would use infrared and/or visible spectrum light.
  • Light Amplification by Stimulated Emission of Radiation- (LASER).
  • Properties of Lasers
    • Produce monochromatic light of extremely high intensity.
t he operation of the laser6
The operation of the Laser

(Pumping the Laser)

t he operation of the laser8
The operation of the Laser

Spontaneous emission

t he operation of the laser9
The operation of the Laser

Spontaneous emission

  • Incoherent light
  • Accidental direction
t he operation of the laser11
The operation of the Laser

Stimulated emission

t he operation of the laser12
The operation of the Laser

Light: Coherent, polarized

The stimulating and emitted photons have the same:

frequency

phase

direction

slide13

Two level system

E2

E2

hn

hn

hn

absorption

Spontaneous emission

Stimulated emission

E1

E1

hn =E2-E1

slide14

E2

E1

Boltzmann’s equation

example: T=3000 K E2-E1=2.0 eV

  • n1 - the number of electrons of energy E1
  • n2 - the number of electrons of energy E2
slide15

Einstein’s coefficients

Probability of stimulated absorption R1-2

R1-2 = r (n) B1-2

Probability of stimulated and spontaneous emission :

R2-1 = r (n) B2-1 + A2-1

assumption: n1 atoms of energy e 1 and n2 atoms of energy e 2 are in thermal equilibrium at temperature T with the radiation of spectral density r (n):

n1 R1-2 = n2 R2-1 n1r (n) B1-2 = n2 (r (n) B2-1 + A2-1)

E2

E1

slide16

According to Boltzman statistics:

  • r (n) = =

Planck’s law

B1-2/B2-1 = 1

slide17

The probability of spontaneous emission A2-1 /the probability of stimulated emission B2-1r(n ):

  • Visible photons, energy: 1.6eV – 3.1eV.
  • kT at 300K ~ 0.025eV.
  • stimulated emission dominates solely when hn /kT <<1!
  • (for microwaves: hn <0.0015eV)
  • The frequency of emission acts to the absorption:
  • if hn /kT <<1.

x~ n2/n1

slide18

E2

E1

Condition for the laser operation

Ifn1 > n2

  • radiation is mostly absorbed absorbowane
  • spontaneous radiation dominates.

if n2>> n1 - population inversion

  • most atoms occupy level E2, weak absorption
  • stimulatedemission prevails
  • light is amplified

Necessary condition:population inversion

slide19

E2

E1

How to realize the population inversion?

Thermal excitation:

impossible.

The system has to be „pumped”

Optically,electrically.

slide20

The Uncertainty Principle

Measurement disturbes the system

the uncertainty principle
The Uncertainty Principle
  • Classical physics
    • Measurement uncertainty is due to limitations of the measurement apparatus
    • There is no limit in principle to how accurate a measurement can be made
  • Quantum Mechanics
    • There is a fundamental limit to the accuracy of a measurement determined by the Heisenberg uncertainty principle
    • If a measurement of position is made with precision Dx and a simultaneous measurement of linear momentum is made with precision Dp, then the product of the two uncertainties can never be less than h/2p
the uncertainty principle22
The Uncertainty Principle

Virtual particles: created due to the UP

slide23

The laser operation

Three level laser

E3

Fast transition

E2

Laser action

E1

  • 13 pumping
  • spontaneous emission 3 2.
  • state 2 is a metastable state
  • population inversion between states 2 and 1.
  • stimulated emission between 2 i 1.
slide24

E3

szybkie przejścia

The laser operation

E2

akcja laserowa

E1

- optical pumping - occupation of E3 of a short life time,

10-8s. It is a band, the metastable and ground states are narrow :

-  electrons are collected on E2: population inversion

-   stimulated emission (one photon emitted spontaneously starts the stimulated radiation )

- Beam of photons moves normally to the mirrors – standing wave.

slide26

ruby laser

  • discovered in 60-ies of the XX century.
  • ruby (Al2O3) monocrystal, Crdoped.
slide27

4T1

2T2

Energy

4T2

2E

LASING

4A2

Ruby laser

  • Akcja laserowa z jonów Cr3+, zawartych w rubinie .
  • Laser trzypoziomowy.

Al2O3

  • optical pumping: 510-600nm and 360-450nm.
  • fast transition on 2E.
  • lasing: 2E on4A2,
  • 694nm

Cr+

rapid decay

ruby laser
Ruby laser

First laser: Ted Maiman

Hughes Research Labs

1960